Question

If the position vectors of P and Q are $(\mathbf{i} + 3\mathbf{j} - 7\mathbf{k})$ and $(5\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}),$ then $|\overset{\rightarrow}{PQ}|$ is

• A. $\sqrt{158}$
• B. $\sqrt{160}$
• C. $\sqrt{161}$
• D. $\sqrt{162}$

Answer 1

Answer: (D)

$\sqrt{162}$

Answer 2

$\overline{PQ} = (5 - 1)\mathbf{i} + ( - 2 - 3)\mathbf{j} + (4 + 7)\mathbf{k} = 4\mathbf{i} - 5\mathbf{j} + 11\mathbf{k}$

$|\overline{PQ}| = \sqrt{16 + 25 + 121} = \sqrt{162}.$